Calculate the normal force acting on an object resting on a flat or inclined surface. Enter the object's mass, the gravitational acceleration, and the surface angle — and get the normal force (F_N) in Newtons. Optionally add an external force (applied at an angle) to account for pushing or pulling scenarios.
Normal Force (F_N)
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Weight Force (W = mg)
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Gravitational Component (perpendicular)
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External Force Component (perpendicular)
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Normal force is the perpendicular contact force that a surface exerts on an object resting on it. It acts in the direction opposite to the gravitational component pressing into the surface. The name 'normal' refers to its perpendicular direction — not to anything being 'typical' or 'standard'.
On a flat horizontal surface with no external forces, the normal force equals the object's weight: F_N = m × g. For a 10 kg object on Earth, that's 10 × 9.81 = 98.1 N. If an external force pushes the object down or pulls it up, you add or subtract that vertical component accordingly.
On an inclined surface at angle α, only the component of gravity perpendicular to the surface must be balanced. The formula is F_N = m × g × cos(α). As the angle increases, less of the weight acts into the surface, so the normal force decreases. At 90°, the normal force would be zero.
Not always. On a flat surface with no other forces, they are equal. But on an incline, normal force equals m×g×cos(α), which is less than the full weight. If an external force pushes the object into the surface or lifts it, the normal force changes accordingly. They are only equal in the simplest flat-surface, no-external-force scenario.
In practice, no — a surface can push against an object but cannot pull it. If your calculation yields a negative normal force, it means the object would lift off the surface rather than remaining in contact. In that scenario, the actual normal force is zero, not negative.
When an external force acts on the object, its perpendicular component either adds to or subtracts from the normal force. If you push an object down onto a surface at angle θ below horizontal, F_N = m×g×cos(α) + F_ext×sin(θ). If the force pulls upward, the sin component is subtracted, reducing the normal force.
Normal force is measured in Newtons (N), the SI unit of force. One Newton is defined as the force required to accelerate a 1 kg mass at 1 m/s². You can convert to kN (kilonewtons) by dividing by 1000, or to pound-force (lbf) by dividing by 4.448.
Using F_N = m × g, the normal force is 0.6 × 9.81 = 5.886 N. The table pushes up on the book with roughly 5.89 N to counteract gravity and keep the book at rest. This is a direct example of Newton's Third Law in action.